T Test

One sample t-test is used to match the mean of single sample data to a known or hypothetical population mean. The one sample t-test is a constant quantity test. This test is also known as a single sample t-test. Where t is the variable. Common use of one sample t-test One sample t-test is generally used to test the following- Statistical difference between a variable score and a zero.Statistical value from a mean value to a known or hypothesized value of the mean in the population. Single sample t-test will compare only a single sample mean to a specified constant instead of comparing sample mean between two or more groups. Data Requirement for one sample t-test To calculate the single t-test your data must meet following requirements: A continuous test variable (t)Independent scores of test variables.Random sample of population dataNormal distribution of the sample and population on the test valueHomogeneity of variances.No outliers One sample t-test example Let’s take an example from your business sales department. Question: You want to improve a sales performance report. In the past years your sales were $100 per transaction. This year after training, your sales data indicates mean sales of $130 with a sample of twenty five sales persons with a standard deviation of $15. Did the training give any result to you? Test the hypothesis at a 5% alpha level. Solution: Step 1: Null hypothesis value: where there is no increase in sales H0: μ $100. Step 2: Alternate hypothesis: where there is increase in sales H1: μ > $100. Step 3: According to question: The sample mean(x̄). This is often given within the question as $130.The population mean(μ). Given as $100 (from past data).The sample standard deviation(s) $15.Number of observations(n) 25. Step 4: t-score formula says: t (130 – 100) / ((15 / √(25)) t (30 / 3) 10 This is your calculated t-value. Step 5: Find T-table values. To find t-table value we need two variables: Alpha value i.e 5% given in the questions aboveDegrees of freedom i.e. number of items in the sample minus 1 t:25-124 According to the above distribution table; the intersection of degrees of freedom and alpha is 1.711. Conclusion There is a significant difference between our hypothesis t-value and distribution t-table value does not fall in the range calculated above in step 4 and step 5. So we will reject the null hypothesis. This means your sales training got success as its value is greater.

T Test

How do you Calculate a One Sample T Test?